The equivalence of “strong calmness” and “calmness” in optimal control theory |
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Authors: | R.B Vinter |
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Affiliation: | Department of Electrical Engineering, Imperial College, London SW7 2BT, England |
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Abstract: | In an earlier paper optimality conditions expressed in terms of a Lipschitz continuous function which satisfies a condition resembling the Hamilton-Jacobi-Bellman equation were derived. It was shown that a certain hypothesis, strong calmness, is the weakest hypothesis under which such developments are possible. In the present paper it is shown that strong calmness is equivalent to calmness for a wide class of problems. Support is thereby given to strong calmness as being a reasonable hypothesis, since calmness is apparently the weakest known hypothesis assuring normality, in the sense that the Pontryagin maximum principle applies with the cost multiplier nonzero. |
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